Microscopic model. We first perform 2D Brownian dynamics-Monte
Carlo (BD-MC) simulations of MTs driven by explicit motors with
binding/unbinding kinetics [1]}. The main purpose is to
quantify local MT pair interactions, with long-ranged hydrodynamics
neglected due to its high computational cost. We represent MTs as
perfectly rigid rods, and assume a reservoir of ideal motors at fixed
chemical potential. The motors bind to (unbind from) two filaments
simultaneously, and unbind immediately upon reaching the plus end of
either MT. At equilibrium, the average number of motors crosslinking
MTs \(i\)  and \(j\)  is \(\left\langle N_{ij} \right\rangle \sim \rho ^2 \int ds_{i} \int ds_{j} \exp {\left[-\frac{u_{c}(s_{i},s_{j})}{k_{B} T}\right]}\) , where
\(\rho \)  is the linear binding-site density on a single MT, \(u_c\)  is the
quadratic potential for crosslinks extension, and \(s_{i,j}\) 
parametrizes the MT arclength [1]}. The number of motors that
bind/unbind is sampled from a Poisson distribution with the correct
average number of events at each time interval so that the equilibrium
distribution is recovered for static crosslinks. Bound motors are
inserted by first selecting pairs of MTs then sampling from the
appropriate bivariate normal distribution to choose motor endpoints.
The motor on each crosslink endpoint moves with a linear
force-velocity relation [3]}:
\(v=v_m\max (0,\min (1,1+f/f_s))\) , where \(f\)  is the
magnitude of the crosslinking force, \(v_m\)  is the maximum
translocation velocity, and \(f_s\)  is the stall force. After the MC
cycle, we compute all the forces and torques from motors, short-range
repulsion, anisotropic local fluid drag by the solvent, and random
thermal forces, to evolve MT positions and orientations forward in
time [4]}, [1]}. The BD-MC simulations are
nondimensionalized using the length \(b\) , energy \(k_B T\) , and time
\(\tau = D/b^2\) , where \(D\)  is the diffusion coefficient of a sphere of
diameter \(b\) . Our model is similar to that of Head et al.
[6]}, but new in our work are algorithmic improvements for
handling crosslinks and neglect of filament elasticity that allow us
to simulate larger systems and measure the stress tensor.
